Diffusion of the Emanations.
160. It has been shown that the emanations of thorium and radium behave like radio-active gases, distributed in minute amount in the air or other gas in which they are tested. With the small quantities of active material so far investigated, the emanations have not yet been collected in sufficient amount to determine their density. Although the molecular weight of the emanations cannot yet be obtained by direct chemical methods, an indirect estimate of it can be made by determining the rate of their inter-diffusion into air or other gases. The coefficients of inter-diffusion of various gases have long been known, and the results show that the coefficient of diffusion of one gas into another is, for the simpler gases, approximately inversely proportional to the square root of the product of their molecular weights. If, therefore, the coefficient of diffusion of the emanation into air is found to have a value, lying between that of two known gases A and B, it is probable that the molecular weight of the emanation lies between that of A and B.
Although the volume of the emanation given off from radium is very small, the electrical conductivity produced by the emanation in the gas, with which it is mixed, is often very large, and offers a ready means of measuring the emanation present.
Some experiments have been made by Miss Brooks and the writer[[253]] to determine the rate of the diffusion of the radium emanation into air, by a method similar to that employed by Loschmidt[[254]] in 1871, in his investigations of the coefficient of inter-diffusion of gases.
Fig. 56.
[Fig. 56] shows the general arrangement. A long brass cylinder AB, of length 73 cms., and diameter 6 cms., was divided into two equal parts by a moveable metal slide S. The ends of the cylinder were closed with ebonite stoppers. Two insulated brass rods, a and b, each half the length of the tube, passed through the ebonite stoppers and were supported centrally in the tube. The cylinder was insulated and connected with one pole of a battery of 300 volts, the other pole of which was earthed. The central rods could be connected with a sensitive quadrant electrometer. The cylinder was covered with a thick layer of felt, and placed inside a metal box filled with cotton wool in order to keep temperature conditions as steady as possible.
In order to convey a sufficient quantity of emanation into the half-cylinder A, it was necessary to heat the radium slightly. The slide S was closed and the side tubes opened. A slow current of dry air from a gasometer was passed through a platinum tube, in which a small quantity of radium compound was placed. The emanation was carried with the air into the cylinder A. When a sufficient quantity had been introduced, the stream of air was stopped. The side tubes were closed by fine capillary tubes. These prevented any appreciable loss of gas due to the diffusion, but served to keep the pressure of the gas inside A at the pressure of the outside air. The three entrance tubes into the cylinder, shown in the figure, were for the purpose of initially mixing the emanation and gas as uniformly as possible.
After standing several hours to make temperature conditions steady, the slide was opened, and the emanation began to diffuse into the tube B. The current through the tubes A and B was measured at regular intervals by an electrometer, with a suitable capacity in parallel. Initially there is no current in B, but after the opening of the slide, the amount in A decreased and the amount in B steadily increased. After several hours the amount in each half is nearly the same, showing that the emanation is nearly uniformly diffused throughout the cylinder.
It can readily be shown[[255]] that if
K = coefficient of diffusion of the emanation into air,
t = duration of diffusion experiments in secs.,
a = total length of cylinder,
S1 = partial pressure of emanation in tube A at end of diffusion,
S2 = partial pressure of emanation in tube B at end of diffusion,
then
Now the values of S1 and S2 are proportional to the saturation ionization currents due to the emanations in the two halves of the cylinder. From this equation K can be determined, if the relative values of S1 and S2 are observed after diffusion has been in progress for a definite interval t.
The determination of S1 and S2 is complicated by the excited activity produced on the walls of the vessel. The ionization due to this must be subtracted from the total ionization observed in each half of the cylinder, for the excited activity is produced from the material composing the emanation, and is removed to the electrodes in an electric field. The ratio of the current due to excited activity to the current due to the emanation depends on the time of exposure to the emanation, and is only proportional to it for exposures of several hours.
The method generally adopted in the experiments was to open the slide for a definite interval, ranging in the experiments from 15 to 120 minutes. The slide was then closed and the currents in each half determined at once. The central rods, which had been kept negatively charged during the experiments, had most of the excited activity concentrated on their surfaces. These were removed, new rods substituted and the current immediately determined. The ratio of the currents in the half cylinders under these conditions was proportional to S1 and S2, the amounts of emanation present in the two halves of the cylinder.
The values of K, deduced from different values of t, were found to be in good agreement. In the earlier experiments the values of K were found to vary between ·08 and ·12. In some later experiments, where great care was taken to ensure that temperature conditions were very constant, the values of K were found to vary between ·07 and ·09. The lower value ·07 is most likely nearer the true value, as temperature disturbances tend to give too large a value of K. No certain differences were observed in the value of K whether the air was dry or damp, or whether an electric field was acting or not.
161. Some experiments on the rate of diffusion of the radium emanation into air were made at a later date by P. Curie and Danne[[256]]. If the emanation is contained in a closed reservoir, it has been shown that its activity, which is a measure of the amount of emanation present, decreases according to an exponential law with the time. If the reservoir is put in communication with the outside air through a capillary tube, the emanation slowly diffuses out, and the amount of emanation in the reservoir is found to decrease according to the same law as before, but at a faster rate. Using tubes of different lengths and diameters, the rate of diffusion was found to obey the same laws as a gas. The value of K was found to be 0·100. This is a slightly greater value of K than the lowest value 0·07 found by Rutherford and Miss Brooks. No mention is made by Curie and Danne of having taken any special precautions against temperature disturbances, and this may account for the higher value of K obtained by them.
They also found that the emanation, like a gas, always divided itself between two reservoirs, put in connection with one another, in the proportion of their volumes. In one experiment one reservoir was kept at a temperature of 10° C. and the other at 350° C. The emanation divided itself between the two reservoirs in the same proportion as would a gas under the same conditions.
162. For the purpose of comparison, a few of the coefficients of inter-diffusion of gases, compiled from Landolt and Bernstein’s tables, are given below.
| Gas or vapour | Coefficient of diffusion into air | Molecular weight |
|---|---|---|
| Water vapour | 0·198 | 18 |
| Carbonic acid gas | 0·142 | 44 |
| Alcohol vapour | 0·101 | 46 |
| Ether vapour | 0·077 | 74 |
| Radium emanation | 0·07 | ? |
The tables, although not very satisfactory for the purpose of comparison, show that the coefficient of inter-diffusion follows the inverse order of the molecular weights. The value of K for the radium emanation is slightly less than for ether vapour, of which the molecular weight is 74. We may thus conclude that the emanation is of greater molecular weight than 74. It seems likely that the emanation has a molecular weight somewhere in the neighbourhood of 100, and is probably greater than this, for the vapours of ether and alcohol have higher diffusion coefficients compared with carbonic acid than the theory would lead us to anticipate. Comparing the diffusion coefficients of the emanation and carbonic acid into air, the value of the molecular weight of the emanation should be about 176 if the result observed for the simple gases, viz. that the coefficient of diffusion is inversely proportional to the square root of the molecular weights, holds true in the present case. Bumstead and Wheeler[[257]] compared the rates of diffusion of the radium emanation and of carbon dioxide through a porous plate, and concluded that the molecular weight of the emanation was about 180. On the disintegration theory, the atom of the emanation is derived from the radium atom by the expulsion of one α particle. Thus, it is to be expected that its molecular weight would be over 200.
It is of interest to compare the value of K = ·07 with the value of K determined by Townsend ([section 37]) for the gaseous ions produced in air at ordinary pressure and temperature, by Röntgen rays or by the radiations from active substances. Townsend found that the value of K in dry air was ·028 for the positive ions and ·043 for the negative ions. The radium emanation thus diffuses more rapidly than the ions produced by its radiation in the gas, and behaves as if its mass were smaller than that of the ions produced in air, but considerably greater than that of the air molecules with which it is mixed.
It is not possible to regard the emanation as a temporarily modified condition of the gas originally in contact with the active body. Under such conditions a much larger value of K would be expected. The evidence derived from the experiments on diffusion strongly supports the view that the emanation is a gas of heavy molecular weight.
Makower[[258]] has recently attacked the question of the molecular weight of the radium emanation by another method. The rate of diffusion of the emanation through a porous plug of plaster-of-Paris was compared with that of the gases oxygen, carbon dioxide, and sulphur dioxide. It was found that Graham’s law, viz. that the coefficient of diffusion K is inversely proportional to the square root of its molecular weight M, was not strictly applicable. The value of K √M was not found to be constant for these gases, but decreased with increase of molecular weight of the gas. If, however, a curve was plotted with K √M as ordinate and K as abscissa, the points corresponding to the values of O, CO2 and SO2 were found to lie on a straight line. By linear extrapolation, the molecular weight of the emanation was estimated. The value obtained from experiments on three different porous plugs was 85·5, 97, and 99 respectively. This method indicates that the molecular weight of the radium emanation is about 100; but in all the experiments on diffusion, it must be remembered that the emanation, whose rate of inter-diffusion is being examined, exists in minute quantity mixed with the gas, and is compared with the rate of inter-diffusion of gases which are present in large quantity. For this reason, deductions of the molecular weight of the emanation may be subject to comparatively large errors, for which it is difficult to make correction.